07] 

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234 

ag UNIVERSITY OF ILLINOIS 


Agricultural Experiment Station 


BULLETIN No. 234 


A GRAPHICAL PRESENTATION OF THE 
FINANCIAL PHASES OF FEEDING 
EXPERIMENTS 


By H. H. MITCHELL 


5 
y 3 


) 
! 


URBANA, OCTOBER, 1921 


CONTENTS OF BULLETIN No. 234 


PAGE 

INTRODUCTION © 0%. 95 ciclac 0 a.0 0 wae bv eieneta atarerete cote cele ete teen 271 
A GENERAL STATEMENT OF THE PROBLEM. .........0. +) see 274 
CHARTS INVOLVING TWO VARIABLE FACTORS... ... 3. .2. see 275 
AN ILLUSTRATION IN SHEEP FEEDING...........-. +a s01c\s pennies 276 
WHEN Lot GAINS ARE NEARLY EQUAL..............005 5 ae 283 
ILLUSTRATIONS IN SWINE FEEDING (li 00505004 saad ss tae 283 
CHARTS INVOLVING THREE VARIABLE FACTORS. ... 2)... 297 
AN ILLUSTRATION IN STEER FEEDING............. WE  . 297 

AN ILLUSTRATION IN. SWINE FEEDING. .....0.000- s+ 0+." see 298 


CHARTS INVOLVING MORE THAN THREE VARIABLE FACTORS.... 303 
ILLUSTRATIONS IN MILK PRODUCTION. .<.«seee-ceess sue ye ess + oe 303 


ILLUSTRATIONS IN STEER PEEDING......¢.csecst cass ecuen ele 0 en 304 


CHARTS PERMITTING GREATER FLEXIBILITY IN FINANCIAL 
PREDICTIONS 2s cccceccacaece sve doacteeis oslo dah 


ILLUSTRATIONS IN STEER FEEDING. .:.......2... ca «aes ee a)cneneneen 315 


SUGGESTIONS FOR INCREASING THE PRECISION OF FINANCIAL 
ESTIMATES oo: 0 dcce o nye cco clea a du biate aheh elilp (elo mnubats Nene (oot 316 
APPENDIX (Construction of charts) (2... 20... s fs00 us «cso wns een 318 


A GRAPHICAL PRESENTATION OF THE 
FINANCIAL PHASES OF FEEDING 
EXPERIMENTS 


By H. H. MITCHELL, Associate CHIEF IN ANIMAL NUTRITION 


INTRODUCTION 


In the ordinary type of feeding experiment there are essentially 
three experimental results; namely, the rate of gain of the animals, 
the economy of gain expressed in terms of the ration tested, and the 
market finish produced. The first two items can be measured accu- 
rately in any particular feeding operation, tho they are subject to a 
variable and oftentimes considerable experimental error when con- 
sidered as experimental data. The third item is not susceptible of 
exact measurement and can be described only by stating the grade of 
butcher stock as judged by competent buyers, or its selling price per 
hundredweight relative to the prevailing market prices. 

All statements made of the monetary cost of gains and of the profits 
returned from any experimental feeding operation are necessarily not 
experimental results, since they depend so largely upon factors not. 
under experimental control and not subject to any predictable varia- 
tion, i. e., the prevailing market prices of feeds and live stock. The 
economy of any system of feeding, expressed in terms of commodities, 
has a permanent value; whereas when expressed in terms of financial 
profits or losses for any given set of prices, it will have little if any 
value. The latter expression is, and should be, of interest only to the 
experiment station conducting the work, and then only as an item in 
its ledger accounts. 

In spite of these facts, it is in general only the financial phases of 
experimental feeding operations that are of primary interest to the 
live-stock farmer. Hence the universal custom of including financial 
statements, sometimes in minute detail, in reports of feeding experi- 
ments, showing how and why the experiment station gained or lost 
money on each experimental lot, and what such profit or loss amounted 
to per head. Generally these financial matters find their way into the 
summary and conclusions of the bulletin, sometimes even to the exelu- 
sion-of the bona fide experimental results themselves. In any ease, 
it is very often found that such financial statements receive the main 
emphasis in the accompanying discussion. 

The emphasis accorded the cost of experimental feeding operations, 
and the profits or losses realized, seems to be due to the undoubted 


271 


272 BULLETIN No. 234 [ October, 


demand for such information from practical live-stock men and also 
to the fact that a practical comparison of the economy of the different 
feeding operations under trial cannot be made upon any other basis. 
A discussion of the results of a series of experiments based entirely 
upon the feed consumption and the gains secured would be barren of 
interest to readers desiring information on the most economical meth- 
ods of feeding live stock, unless supplemented by calculations of re- 
ceipts and expenditures, probable profits and necessary margins, and 
the like, calculations, which many readers are reluctant to make be- 
cause they are not always straight-forward arithmetical calculations 
and often are time-consuming. 

The difficulties in meeting the justifiable demand for some consid- 
eration of the financial aspects of experimental feeding operations are 
well stated by Forbes:* ‘‘It is impossible to make a statement of the 
financial outcome of such a comparison of feeds, which will be at the 
same time useful and true. The reason is that market conditions are 
never the same at two different times, or in two different places. The 
relative prices of feeds today, in any given market, do not apply in any 
other market, and in all probability will never again recur.”’ 

Attempts are frequently made to overcome in part the unanswer- 
able objections to the unmodified ‘‘financial statement’’ of a feeding 
experiment, mainly in the direction of computations of the effect of 
variations in the prices of feeds on the profits or losses per head. A 
fairly satisfactory result may be secured with rations containing only 
two feeds, if the additional mass of tabulated figures is not considered 
to be detrimental; but with rations including three or more feeds, 
complicated and less serviceable tables result. Everything considered, 
this method of modifying the financial statement is not to be recom- 
mended. The large amount of tabulated data resulting must seem 
formidable to one not used to the study of figures, and it may require 
considerable study to discover just how to enter the tables to obtain 
values corresponding to any particular set of prices. Furthermore 
the accurate use of such a table must involve ordinarily two or more 
interpolations, since any prevailing set of feed prices will not in gen- 
eral correspond to the arbitrary prices used in the compilation of the 
table. 

In general no systematic attempt is made to determine the effect of 
variations in the cost of feeders and in the margin of selling price over 
cost, on the profits or losses to be expected in steer and sheep feeding 
operations. And yet fluctuations in the live-stock market have a 
preponderating effect in determining the success or failure of the live- 
stock business. The financial result of the simplest steer or sheep 
feeding operation (and occasionally of swine feeding operations) de- 


*Forbes, E. B., Specific Effects of Rations on the Development of Swine. 
Ohio Agr. Exp. Sta, Bul. No. 213. 1909. 


192i | FINANCIAL PHASES OF FEEDING EXPERIMENTS 273 


pends upon four main factors, no two of which can be considered to be 
sufficiently correlated to permit of simplification; these factors are: 
(1) the cost of feeders per hundredweight; (2) the margin of selling 
price per hundredweight over cost; (3) the cost of a cereal or nitrc- 
genous concentrate; and (4) the cost of a roughage. No tabulated 
computations can adequately deal with values influenced by four in- 
dependent variables, and when the number of variables increases as 
the rations used increase in complexity, any method heretofore tried, 
as far as the author is aware, fails completely. Swine feeding opera- 
tions are generally less difficult to deal with in the formulation of 
flexible financial statements suitable for use under variable market 
conditions, since ordinarily in computing profits and losses from such 
undertakings only the cost and selling price of the pork produced is 
considered. But even here the tabulated values based on a sliding 
scale of feed prices cannot be used with accuracy unless interpolation 
is resorted to. 

The nature of the problem of giving a proper financial interpreta- 
tion to experimental feeding data suggests the use of graphical meth- 
ods, the main advantages of which are four. In the first place, they 
do away entirely with large masses of tabulated figures, always con- 
fusing to one not used to the study of numerical data. Secondly, they 
may be used for any values of the variables involved without the 
necessity of interpolation. Again, they afford a sort of bird’s-eye view 
of the situation, a more or less clear visual representation of the effect 
of variation in the market prices of commodities on the value under 
consideration. And, finally, it is possible and entirely feasible in most 
cases, to superimpose charts representing different experimental lots, 
upon one another, and thus to afford ready means of comparison. The 
- method also possesses the considerable advantage of being economical 
of space: 

In this study an attempt has been made to apply a few graphical 
methods’ to the problem under consideration. The methods selected 
and illustrated in the following pages may be used with accuracy, 
and in many eases afford a quick and simple method of perform- 
ing complicated arithmetical calculations. Many of them are 
undoubtedly simple enough to be used in experiment station bul- 
letins. Possibly some hesitation might be felt in including some 
of them in the ordinary bullétin for general distribution. It is 
hoped that all of them, however, will be found to have a distinct 
field of usefulness, and when not considered well adapted to bul- 
letins will in any case be of service to extension workers, farm ad- 


*Deming, H. G., A Manual of Chemical Nomography. University Press, 
Champaign, Ill., 1918. For a more pretentious and exhaustive presentation of 
nomographic methods see ‘‘Graphical and Mechanical Computation,’’ by Joseph 
Lipka. John Wiley and Sons, New York, 1918. 


274 BULLETIN No. 234 [ October, 


visers, editors of farm papers and journals, and to all who are fre- 
quently called upon to aid the live-stock farmer in choosing well-bal- 
anced and economical rations with due regard to the feeds available, 
the prevailing market prices, and the probable fluctuations in market 
conditions during the fattening operation. The value of the methods 
in classroom work will be obvious. 


A GENERAL STATEMENT OF THE PROBLEM 


The financial aspect of a feeding operation is naturally resolved 
into the net receipts’ from the animal when sold and expenditures in- 
eurred in the fattening process. Of the latter the feed bill constitutes 
by far the larger fraction, and in computing profits or losses is gen- 
erally the only item considered. The less important items of expense, 
such as labor, interest, veterinary service, loss of stock by disease or 
accident, depreciation in buildings and other equipment, insurance, 
ete., are offset in part, if not entirely, by receipts from the animal 
other than cash, such as manure and, in the case of steer feeding on 
heavy corn rations, pork produced from the droppings. 

A farmer considering whether or not to fatten live stock during a 
given season, or to sell his grain directly; or, how much stock to fatten 
and on what rations, has before him the following more or less exact 
information. He knows fairly closely what feeder animals will cost 
him in his feed lot; he knows what feeds are most available to him, as 
well as something of their quality and their current prices, that is, 
what he ean sell his home-grown feed for, and what imported feeds 
will cost him. The information he must obtain by ealeulation or by 
less certain methods is: (1) his feed bill per head; (2) the necessary 
margin to cover his expenditures; and (3) considering a probable 
safe margin in view of the present live-stock market and its tendencies, 
his probable profit per head. The latter, in turn, he may compute as 
interest on the money invested or otherwise tied up in the venture, or 
as returns from his home-grown feeds in comparison with their possible 
selling price, or as some other value. 

The financial presentation of the results of experimental feeding 
operations should be such as to aid the practical farmer in these eal- 
culations and approximations, and, in fact, to encourage him in mak- 
ing them. A mere statement of the financial outcome under any given 
set of conditions not only gives him no aid or encouragement along 
these lines, but may actually mislead him into inferring that a sub- 
stantial profit realized by the experiment station, perhaps under un- 
usually favorable market conditions, may be expected under any con- 
ditions. 


*The term ‘‘net receipts’’ is used thruout this paper to mean simply the 
selling price of the animal minus the original cost. 


1921] ‘FINANCIAL PHASES OF FEEDING EXPERIMENTS 275 


CHARTS INVOLVING TWO VARIABLE FACTORS 


Fig. 1 illustrates a method of presenting one side of the question ; 
namely, the net receipts per head under given conditions of cost of 
feeders and margins.” | 

The net receipts per head from steer and sheep fattening opera- 
tions may be conveniently considered as being derived from two 
sources: viz. (1) the increase in market value of the initial weight of 
the animal, which depends of course entirely upon the actual initial 
weight and the margin of selling price per hundredweight over cost; 
and (2) the cash realized on the gain in weight produced, which de- 
pends upon the size of gain and its selling price. This division of the 
net receipts may be stated mathematically as follows: 


r= wm + g (e+m), or 

r =ge -- m (w+g), 
where w is the initial weight of animal; g, the gain per hundred- 
weight; ec, the cost of feeders per hundredweight; m, the margin per 
hundredweight; and r, the net receipts. It is evident, for example, 
from this equation that for a given margin the net receipts will vary 
directly with the cost of feeders; or, in other words, for a given mar- 
gin and feed bill the profits of a feeding operation will increase as the 
cost of feeders increases, simply because the gains will be marketed at 
a higher figure. 

It will be noted that Fig. 1 presents the results of a venture in 
baby-beef production in which the calves were raised at home instead 
of being bought on the market. In computing the net receipts of the 
baby-beef operation, the scale at the left, therefore, instead of repre- 
senting the cost of feeders, as it would in most feeding operations, rep- 
resents the price that the calves might have brought if disposed of di- 
rectly instead of being fattened. The scale on the right represents the 
margin of the selling price per hundredweight of baby beef produced 
over the possible selling price of the unfattened calves. The intermedi- 
ate scale, derived from the data given at the head of the chart, repre- 
sents the net receipts realized per head; or, from another point of 
view, the maximum cost of the feeding operations consistent with no 
loss or profit. Points on the intermediate scale correspond to any 
two points on the side scales situated on the same straight line. 

The chart is used by placing a ruler, stretched string, or other 
straight-edge, across it connecting any value for cost of feeders, on the 
left scale, with the size of margin, on the right, and reading off the 

*The charts explained and discussed in the following pages were constructed 
two or three years ago, when the prices of feeds and of live stock were at the 
highest levels; hence the wide range of prices on the scales of all charts and the 
high prices chosen in illustrating the method. The fact that practically all the 


charts are still serviceable when the prices of farm products have dropped enor- 
mously is a commentary on the great flexibility of the graphical methods used. 


276 BULLETIN No. 234 [October, 


point of intersection on the intermediate scale. For example, if the 
possible selling price of the calves was $12 per hundredweight and the 
baby beef sold at a $5.00 margin, the net receipts per head, as indi- 
eated by the line drawn across the chart connecting these two values 
on their respective scales, would be something less than $127.50— 
approximately $127.30. This value also may be considered as the maxi- 
mum feed bill consistent with no loss or profit. Every dollar the feed 
bill falls short of this value represents a dollar profit, if incidental 
expenditures are left out of consideration. 

The chart may be used also in computing the necessary margin 
in a feeding venture. Suppose the feed consumed per head in this 
fattening operation should be found to cost at prevailing prices 
$127.30. Then the straight-edge will be set at this value on the inter- 
mediate scale and on the point on the left scale corresponding to the 
possible selling price of the calves, say $12.00. Then the point of inter- 
section on the right scale gives the necessary margin to just cover 
expenses, in this case $5.00. 


AN ILLUSTRATION IN SHEEP FEEDING 


Inspection of Fig. 1 shows the possibility of placing several inter- 
mediate scales, representing different experimental lots, between the 
same two principal scales, affording a ready method of comparing lots, 
and incidentally economizing space. It is also evident that the same 
alignment-chart principle illustrated here may be applied to the com- 
putation of feed bills for rations consisting of two feeds, under a wide 
range of price conditions. These statements are illustrated by Figs. 2 
and 3, which together constitute a complete financial interpretation of 
the sheep feeding results upon which they are based. 

Fig. 2 permits of rapid estimation of the total feed bill per head - 
for each lot, with a wide range of prices for each of the feeds used 
(corn and alfalfa hay). As in Fig. 1, the principal scales are at the 
sides; here they represent a serviceable range in price for each feed. 
There is an intermediate scale for each of the four lots. By laying a 
straight-edge across the chart in such a way as to intersect the side 
scales at points corresponding to the prevailing prices of corn and 
alfalfa hay, the feed bill per head for each lot may be read off the 
corresponding intermediate scale. The cross line drawn in, intersect- 
ing the side seales at $1.80 corn and $32 alfalfa hay, shows that at these 
prices the feed bill of Lot 1 would be $5.85; of Lot 2, $5.07; of Lot 3, 
$4.52; and of Lot 4, $4.27; as near as the scales can be read. 

Turning now to Fig. 3, the net receipts per head may be similarly 
calculated for any cost of range lambs and any margin of selling price 
per hundredweight over cost. With feeders at $12, and a margin of 
$2.35, the intersecting line drawn thru the chart indicates upon the 
intermediate scales the net receipts per head for the different lots. 


1921] 


FINANCIAL PHASES OF FEEDING EXPERIMENTS 


lowa Buttetin No. I8Il. Basy Beer Propuction 


277 


CALCULATION OF NET RECEIPTS PER HEAD oF BABY BEEVES 


Possible selling 
price of calves 
per cwt. 


$14.50 


14,00 


1500 


AVERAGE INITIAL WEIGHT OF CALVES, 417 LBS. 


Gain oF G26 Bs. in 386 Days 


Net receipts per head, 
or maximum cost of 
feeding operation 
without loss or profit 





Margin of selling price 
of baby beef per cwt. 
over possible selling 

price of calves per cwt. 


6,00 
575 


5.50 


475 
450 
425 
400 
375 


3.50 


4 


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= * 
8 
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1921] 


Cost of corn 
per bushel 
#200 





$1390 


FINANCIAL PHASES OF FEEDING EXPERIMENTS 279 


ILvinois Buttetin No: 167. Fattreninc Western Lames 


CALCULATION OF EXPENDITURE FOR FEED 


AVERAGE FeeED Consumen: 


LOT CorRN ALFALFA Hay 
U. Tons 
| 1.993 0.0552 
2 1682 0.0638 
3 1138 0.0771 
4 0.87! 0.0842 
TOTAL FEED BILL PER HEAD. 
Lots Cost of alfalfa 
\ 2 3 4 hay per 4h 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 281 


ILLinois Buttetin N2167 FATTENING WesTERN LamBs 


CALCULATION OF NET RECEIPTS PER HEAD 


AVERAGE. INITIAL WEIGHT IN ALL LOTS, SOLBS 


AVERAGE GAINS IN 90 DAYS 
Lot |,270|bs.; Lot 2,242 Ibs. ;Lot 3, I94lbs. | Lot 4, 18.3 lbs. 





Cost of lambs Net receipts per head Margin of selling price 

per cwl. Lot | z oe per cwt. over aay VPs 
$3.75 

$350 

$15 $325 
$14 $3.00 
$13 $275 
+ $250 

*Il $225 

%10 $2.00 
$95 $1.75 
56 $1.50 
$7 125 
$6 $1.00 
$5 $0.75 
$0.50 

$0.25 

$0.00 


FIG.3 : 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 283 


Profits per lot for these four values of corn, alfalfa hay, feeders, and 
margin, may be readily calculated by subtraction, as follows: 


Loti Lot? Lot 3 Lot 4 


Net receipts per head (Fig. 3)..........0.. $5.47 $5.08 $4.38 $4.23 
Pecuenil perinead (FIP, 2) se cccccrcres acc 5.35 5.07 4.52 4.27 
Profit per head, by difference........... +$0.12 +$0.01 —$0.14 —$0.04 


Evidently the particular margin chosen for illustration 1 1s or near to 
the necessary margin for each lot. 

If the necessary margin is desired for given values of feed and 
eost of feeders, the procedure is as follows, for, let us say, $1.50 corn, 
$25 alfalfa hay, and $11.50 feeders. Using Fig. 2, we see that the feed 
bill for Lots 1, 2, 8, and 4 for the above prices of feeds is $4.36, $4.10, 
$3.63, and $3.41, respectively. Taking Fig. 3 and placing the straight- 
edge at $11.50 on the left scale and at $4.36 on the intermediate scale 
for Lot 1, we find that the necessary margin for this lot, read off the 
right-hand scale, is $1.32. Placing the straight-edge still at $11.50 on 
the left scale and at $4.10 on the intermediate scale for Lot 2, the neces- 
sary margin is found to be $1.42. Similarly, the necessary margins for 
Lots 3 and 4 are $1.60 and $1.50. Evidently, on the basis of the prices 
used, the system of feeding accorded Lot 1, consisting of a maximum of 
corn, offers better prospects for profit than any other, with Lots 2, 4, 
and 3 following in order. 


WHEN Lot GAINS ARE NEARLY EQUAL 


In experiments in which nearly equal gains are made by different 
lots the inclusion of intermediate scales for the various lots, as in 
Fig. 3, presents some difficulties. This is illustrated by Fig. 4, in 
which are given scales for the calculation of the net receipts per head 
with steers weighing initially 1,000 pounds and gaining 200, 250, 300, 
300, and 400 pounds, respectively. Evidently three or four lots of 
animals gaining within 50 pounds of each other would be represented 
by intermediate scales clustered so close as to render their proper 
graduation and reading difficult. This difficulty may be obviated by 
making single charts for each lot, or by adopting the expedient illus- 
trated in Fig. 5, of using different scales for the cost of the feeders but 
the same scale for margins. ° In this case, the side scales for Lots 1 and 
4, whose gains differed by 65 pounds, are identical, while with Lots 2 
and 3 different scales of cost of feeders are used. While this modifi- 
cation complicates matters somewhat, the chart is just as serviceable 
as the others when understood. 


ILLUSTRATIONS IN SWINE FEEDING 


In swine feeding experiments, in which, very often, the ration 
consists of only two feeds (corn and a supplement), and in which the 


284 BULLETIN No. 234 [ October, 


profits in feeding are ordinarily figured entirely on the cost of gains 
(based only on the feed consumed) and the market price of pork, the 
alignment-chart principle may be used to decided advantage. Take, 
for example, a recent publication of the Michigan Agricultural Col- 
lege’ by Norton, in which different supplements to corn are compared 
on the basis of average figures of the feed consumed per 100 pounds 
of gain, from a large number of feeding trials from different agri- 
cultural experiment stations. The average data thus obtained by 
Norton are given at the top of Fig. 6. The practical application of 
these data must evidently involve variations in the market price of 
eorn and the different supplements. The practical question to be an- 
swered is, What will pork cost in dollars and cents when swine are 
fed according to the rations specified? The question is completely an- 
swered by the accompanying chart. At the extreme left is the seale 
of prices of corn per bushel, at the extreme right the scale of prices of 
supplements per ton, or, in the case of skim milk, per hundredweight. 
The intermediate scales give the cost of gain per 100 pounds when the 
swine are fed according to the ration indicated at the upper end of the 
scale. The cost of gains for corn alone are given on the right side of 
the line serving as the corn price scale. 

As an illustration of the use of the chart, consider the relative cost 
of the gains produced by the six methods of feeding, with prices at 
the following ievels: 


COP. co rele eee wees POR oe er ee ee $ 1.50 per bushel 
Danka vey) Giiae eva tle) cle ee ele eee 110.00 per ton 
iki :milks 4a Fasc h etante as hiss tee nee OO per cwt. 
Middlings 2077.5 septa sae kectem tees ees 55.00 per ton 
Oil: meal ers cs sates ae ais wise a ov Ree eee epee 75.00 per ton 
SOyDeAD Meal. sie ic as sat bisle kre teleet erat eeemmrety 70.00 per ton 


From the left-hand seale it is evident that with corn at $1.50 per 
bushel the corn-alone method would yield pork costing about $13.04. 
By placing the edge of a ruler at $1.50 on the left scale, and at 
$110 on the supplement seale on the extreme right, the point of 
intersection on the corn-and-tankage scale indicates a cost of $12.48 
per hundredweight. Keeping the straight-edge still at $1.50 on the 
corn scale, and shifting the other end to 55 cents on the skim-milk 
seale on the right, brings the point of intersection on the corn-and- 
skim-milk seale at the value $11.47. The other values desired, deter- 
mined in exactly the same way, are $12.87 for corn and middlings, 
$12.03 for corn and oil meal, and $10.65 for corn and soybean meal. 
Evidently a ration of corn and soybean meal furnishes the cheapest 
gain under these conditions, with corn and skim milk next. 


* Norton, H. W., Jr., Feeding Value of Skim Milk for Swine. Mich. Agr. 
Col., Special Bul. 92. December, 1918. 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 285 


Net RECEIPTS PER HEAD FOR FEEDERS WEIGHING 
IOOOLBS. AND GAINING 200-400LBS.IN THE FEED Lot 


Net receipts for gains of 

: o0lb. 
Margin of selling 
price per cwf. 





Cost of feeders 


per cwt. over cost 
214.50 #6.00 
14.00 5.75 
13.50 5.50 
13,00 525 
12.50 3.00 
12.00 4.75 
11.50 4,50 
11,00 425 
10.50 4.00 
10,00 3.75 
2950 3,50 
9,00 325 
650 3.00 
800 2.75 
7.50 2.50 
700 2.25 
650 2,00 


FIG. 4 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 287 


Purpbue Butretin No.220. Steer Feepine IS!I7-1918 
CALCULATION OF NET RECEIPTS PER HEAD oF FAT CATTLE 


lO50.B. FEepERS. FEEDING Perion 120 Days 
AINS : 
Lot |, 212 Ibs. Lot 2,199 Ibs. 


Lot 3,224|bs. Lot4,287|bs. 
Margin of selling price 
per cwt. over cost 
Cost oF Feepers Per Cwr. Net RECEIPTS PER Heap 


Ou LOTS 





land4 . 





14,50 $600 
14.00 5.75 
13.50: 5.50 
1300 525 
12,50 5,00 
12:90 475 
11.50 450 
1L00 425 
10.50 400 
10.00 375 
2.50 350 
200 325 
850 300 

B00 2.75 
7.50 250 
700 2.25 
650 2.00 
600 175 


PbGeo 


- a ie 
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1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 289 


MicniGAN Speciat Buttetin No92 Swine 
CALCULATION OF Cost oF GAIN PER Cwr. 


FeeD Consumep PER |OOtas. or GAIN 





Corn Skimmilk Tankage Middlings Oil Meal Soy bean Meal 
486.5 ie) [@) re) 1@} Oo 
266.9 785.1 ie) fe} oO ie) 
S795 1@)] 425 fe) 0 fe) 
2833 fe) fe) 191.2 ) 0 70¢—~—4130 
377.3 oO ce) ce) SI7 re) 
3085 re) ie) ° ° 681) 
$i25 
Cost OF aac Ai ala eae OF SAIN Price of supplements pet $129 
Price of corn per bu. orn and oil meal Cornand middlings ton_ except skimmi 
By Seis conc] 806 Baar ment Price of skimmilk pecentt | 
| Gorn mand skim mill Bi 


E $115 
cot} 4 110 


105 


$2.00 


55* 100 


95 





90 


85 


60 





75 


70 


65 





35 








1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 291 


The chart is capable of use in another way, such as that suggested 
by Forbes’, namely in answering the question, What is the maximum 
price of supplements at which it would be a matter of indifference 
whether they be used with corn or not? In other words, with corn 
valued at any given price, how much ean one afford to pay for a supple- 
ment and obtain no more expensive gains than if corn were fed alone? 
The chart gives a direct answer to this question, for any price of corn, 
thus saving considerable arithmetic. Take, for example, corn at $1.60 
per bushel. The scale on the right of the corn price scale shows that 
at this price a ration of corn alone will produce pork costing prac- 
tically $13.90 per hundredweight. By placing the ruler at $1.60 on 
the corn price scale and $13.90 on the corn-and-tankage scale, a line 
is defined which intersects the price-of-supplement scale far above the 
highest value given, i. e., at about $145. This means that with corn 
at $1.60 per bushel tankage can be as high as $145 per ton before it 
would become unprofitable as a corn supplement. A line drawn thru 
$1.60 on the corn seale and $13.90 on the corn-and-oil-meal interme- 
diate scale, will intersect the scale at the extreme right at $121, indi- 
eating that this supplement may reach this high value before it be- 
comes unprofitable. For soybean meal, the maximum price would be 
far above the highest price given for supplements; also for skim milk. 
For middlings, the maximum price is the relatively moderate one of 
$60.50. In fact, a glance at the chart shows that this supplement com- 
pares very poorly, at all prices, with the others. Another illustration 
of the use of this chart is to find the price that could be paid for a 
commercial supplement, such as tankage, for given prices of farm 
feeds, corn, and skim milk. If the latter are priced at $1.40 per bushel 
and 45 cents per hundredweight, respectively, it may be readily shown 
by the chart that it would be unprofitable to feed tankage costing 
more than $32 per ton. 

- Of course these considerations neglect entirely the rates of gain. 
The supplements might, as a matter of fact, be profitable to use, at 
values higher than those found, because of the more rapid gain se- 
cured, the saving in labor, and the advantage of an early market. 


1 Forbes, BE. B., Specific Effects of Rations on the Development of Swine. Ohio 
Agr. Exp. Sta. Bul. 213. 1909, 


* Obviously the value of a chart such as Fig. 6 is limited only by the value of 
the experimental data upon which it is based. It is unfortunate, therefore, that 
the average figures given at the top of the chart were apparently obtained by an 
indiscriminate averaging of results not necessarily homogeneous, in so far as one 
may judge from the meager description given of them in the bulletin. The misfor- 
tune is that the data cannot be used with any great confidence for pigs of any given 
weight, such as spring or fall pigs, or for feeding operations resulting in any 
definite market weight of pigs or for dry-lot or pasture feeding. This is a good 
illustration of the fact that averages of even large amounts of data, unless the 
latter are reasonably homogeneous and chosen with discrimination, may be of 
doubtful value and of little praetical utility. 


292 BULLETIN No. 234 [ October, 


Figs. 7 and 8 are other illustrations of the possibilities in the appli- 
eation of the alignment-chart principle to pig feeding problems. Fig. 
7 is a financial interpretation of some results obtained at the Ohio Ex- 
periment Station on the feeding of different proportions of skim milk 
and corn. With corn and skim milk at any given prices, (such as $1.20 
per bushel for corn and 45 cents per hundredweight for skim milk), 
the exact cost of the gains for the different lots may be read off by 
means of a ruler; namely, Lot 3 (corn 1, skim milk 1), $8.52; Lot 4 
(corn 1, skim milk 3), $9.00; Lot 5 (corn 1, skim milk 5), $10.23; 
Lot 6 (corn and skim milk ad libitum), $10.08. The chart might be 
more serviceable if the skim-milk seale were extended to 60 or 65 
cents, to meet a possible increase in the price of this product. 

Fig. 8 is a financial interpretation of the results of another Ohio 
bulletin on the effect of age on the rate and economy of gains. The 
data on which the chart is based are given at the head of the chart 
and represent averages of experiments designated as Nos. 3 and 4, 
with the exception of the first weight group of 50 to 100 pounds, for 
which the data of Experiment 3 only were available. The data of this 
group were obtained from 12 pigs; those for succeeding weight inter- 
vals, from 22, 17, 12, and 5 pigs, respectively. To avoid undue con- 
gestion of the intermediate scales, the scale of tankage prices for the 
last weight interval is moved some distance to the left of the corre- 
sponding scale of the other weights. The use of the chart is illustrated 
by the cross line drawn thru $1.80 corn and $110 tankage. At these 
prices the first 50 pounds of gain was put on at a cost of $10.76 per 
hundredweight; the next hundred at $11.78; the next at $13.57; the 
next at $15.38; and the last hundred, shifting the line to the $110 mark 
on the left tankage scale, was put on at a cost of $16.38. 








1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 293 
OHio Buctetin No. 316 SuPpPpLeEmMeNTs To Corn FoR Swinein Day Lot 
CALCULATION oF Cost PER /00.Bs. oF Gains PRopuceD 

IN. SWINE. 
Five Pies Per Lot Av. INITIAL WelontT=43.7 Les. Fattenine Perioo or 15 WEEKS 
RATIONS— AVERAGE 
Lot (|) PER DAY— (2)PeER 100 LBS. GAIN- DAILY GAIN 
\. 2.40 LBS CORN 685 LBS. CORN 0.35 LBS. 
2. 315 LBS CORN, 0.35 LBS. TANKAGE 350 LBS.CORN, 39LBS.TANKAGE 0.90 
3. 316 LBS. CORN, 315 LBS. SK. MILK 330 LBS. CORN, 330LBS. SK MILK 0.96 
4, 341 LBS. CORN, 10.22 LBS. SK.MILK 257 LBS. CORN, 7T60LBS.SK.MILK 1.33 
5. 3.24 LBS. CORN, 16.18 LBS. SK.MILK 234 LBS. CORN, [I66LBS. SK.MILK 1.39 
6. 3.18 LBS. CORN, 20.53 LBS. SK MILK 200 LBS. CORN,1292 LBS. SK.MILK 1.59 
z - re) infos. 
PRICE & ae m Jen s a x< <x of a. 
or < % < z= 2 = oe 
le) eS = r= x= PRICEOF PRICE OF 
coRN © @e &Z ED) se 0 ea 
PER au. 9 Sx > < oo on OF SK.MILK  TANKAGE 
LoTl ord Lor2 tor4 tor5 Lor6é mee on 
$2.00 —, 120 
?, $14 
1.00 15 
3 
180 A5¢— 110 
170 12 105 
60 A0* 100 
1 
1.50 95 
140 10 35 90 
1.30 85 
iS) 
,20— 30 80 
8 
1.10 15 
1.00 7 254 — 70 
90 65 
6 
¢ 
.80 20 60 
5 
70 8 
60 50 


Gi Gal 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 295 


Onto Butretin No. 335. Errect or Ace or Pics on tHE RATE AND 
Economy oF Gains 


CALCULATION OF THE Cost OF GAINS AT DIFFERENT WEIGHTS 


Feep Consumep Per |OOcBs. of Gain : 
From 50 to l00lbs. 282 |!bs. corn. 507Ibs. tankage 
Wale) “Yal0loy ahi ts ie redo - 







| 
Za 
CncOOmOO0m 
4. * 800 °400“ 425 ° * 904°" 
52). 2) 400! 500) 454. - 5265 

Price of 

Cost oF GAINS PER IOOLBS. 
com per bu 14 Lo (t wane Price OF Ue Seer PER TON 
2.10 


120 


1.10 


1,00 


80 


10 


FIG.8 





ve “Pap! 
as ‘bs * porary. 
'. 


’ ‘ 
' 


. 
>: 
~_ 
. 
“a < 
\ 
. 
: 
. 
= ‘ 
_ ‘a 
= 
' 
f 
Z ' 
© 
bad 
’ 
» 
1 
, i 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 297 — 


CHARTS INVOLVING THREE VARIABLE FACTORS 


We have thus far considered the financial presentation of results 
involving only two variable factors: either (1) the cost of feeders and 
(2) the margin of selling price over cost, in the estimation of the net 
receipts per head, or of the necessary margin for a given feed bill and 
eost of feeders; or the prices of two feeds in estimating the feed bill 
of a ration involving these feeds only. With the presence of three or 
more variable factors, such as are met in estimating the cost of many 
of the common rations used in the fattening of steers, sheep, and 
swine, the graphical interpretation increases somewhat in complexity, 
tho it is still perfectly straightforward and readily followed on brief 
study. 


AN ILLUSTRATION IN STEER FEEDING 


The first illustration of the graphical computation of a feed bill 
involving three feeds is given in Fig. 9. In the chart on the right, 
the cost of the feed bill for Lot 2 may be computed. The ration con- 
sists of three feeds: clover hay, cottonseed meal, and corn silage. In 
this case, the price of corn silage is based on the price of corn, a ton 
of the silage being valued at 6.5 times the price of a bushel of the grain, 
or 0.182 times the price of a ton of corn. The scale on the left repre- 
sents the price of clover hay; the scale at the extreme right represents 
the price of cottonseed meal and corn per ton. The horizontal scale 
at the bottom facilitates the conversion of corn prices from the bushel 
to the ton basis. The use of the chart is best illustrated by an ex- 
ample: With corn at $1.60 per bushel, clover hay at $30 per ton, and 
cottonseed meal at $75 per ton, what will be the feed bill per head for 
Lot 2? From the horizontal scale it is seen that corn at $1.60 per 
bushel is valued at about $57.20 per ton, as near as the scale can be 
read. With a ruler placed at the $30 mark on the clover hay scale, and 
at the $75 mark on the principal scale at the extreme right, a light line 
is drawn until it intersects the intermediate ungraduated line as shown. 
A line is then drawn connecting this point of intersection with the 
$57.20 mark on the principal scale. Where this line intersects the scale 
immediately to the left of the principal scale, the cost of the ration 
($54.00) is indicated. 

The dotted lines on the chart for Lot 1 illustrate the method of com- 
puting the cost of ration for this lot, with corn at $1.60 per bushel, 
clover hay at $30, and cottonseed meal at $73. At these prices, the 
feed consumed per head would cost $63.30, the corn silage being valued 
on the basis of the price of corn, as explained above. 

In the use of these charts. it is not necessary to draw in the lines, 
but simply to indicate, with’ pencil, the intersection points on the 
ungraduated line and on the feed-bill scale. 


298 BULLETIN No. 234 [ October, 


AN ILLUSTRATION IN SWINE FEEDING 


An illustration of the way in which such three-feed charts may be 
superimposed upon one another is presented by Fig. 10, which gives a 
financial interpretation of some unpublished swine feeding data from 
the Illinois Experiment Station. The two side scales, one for tankage 
and the other for corn, middlings, and oats, are used for both lots. 
The body of the chart consists of two ungraduated perpendicular lines 
for the location of intersection points for oats and middlings, respect- 
ively, and two other perpendiculars graduated to give the cost of gain 
per 100 pounds, for each lot. At the bottom of the chart are two 
conversion scales for corn and oats, equating prices per ton and prices 
per bushel. 

The dotted cross lines indicate the use of the chart when corn is 
valued at $1.68 per bushel, or $60 per ton (see lower scale) ; oats 65 
cents per bushel, or approximately $40.50 per ton; tankage at $100 per 
ton; and middlings at $65 per ton. At these prices the cost of 100 
pounds of gain would be $15.00 for Lot 14 and $18.05 for Lot 15. 

The chart may also be used in answering such a question as this: 
With corn and tankage at the prices quoted and middlings at $65, 
how high would oats have to be per ton to raise the cost of pork pro- 
duction in Lot 15 to that of Lot 14; i. e., $15.00? <A straight-edge 
placed on the $60 mark on the right-hand seale and on the $15 mark on 
the feed-bill scale for Lot 15, would intersect the oats ungraduated line 
a short distance above the top horizontal line of the chart. Marking 
this point of intersection after extending the vertical line, and placing 
the straight-edge at this intersection mark and at the $100 mark on the 
tankage seale, and we have a line which cuts the right-hand scale at the 
value sought—in this case, way above the graduations, at almost $90. 
This means that until oats cost as high as $90 per ton it will be more 
profitable to fatten hogs according to the ration of Lot 15 than accord- 
ing to the ration of Lot 14 when the prices of corn and tankage are 
those stated. 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 299 


Purove Butcetin No.220 Winter STEER FEEDING !9!7-18 
CALCULATION OF TOTAL FEED BILL PER HEAD AT VARYING PRICES 


Lor one 
Total feed consumed per sleer: Total feed consumed per sleer : 
\ Shelled corn 428\be Cottonseed meal 336!bs 
Coltonseed meal 335 lbs Corn silage 65II lbs 
Corn silage SG8S\bs. Clover hay 500|bs 


Clover hay 479l|bs. 


Price of corn and Price of cornand 
cottonseed meal per ton. Cottonseed meal per ton 






Price of clover Cottonseed Price of clover Cottonseed 
Pee per ton. mea Corn hay per ton meal 
45 6 $20 


35 


25 


te 
2 
f= 
< 
x 
w 
° 
bE 
oO 
2 
O 


Cost oF RATION 


20 


Price of corn per bu ; 
6eot 70 80 90 100 110 120 130 140 150 160 170 180 190 200 “2.10 


a 


$25 30 35 40 45 50 55 60 65 70 75 
Price of corn per ton 


FIG.9 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 301 


ILuinois Resutts in Swine Feepinc (UnPuBtisHeo) 


CALCULATION OF FEED BILL PER 100 LBS OF GAIN PRODUCED 


291 Ibs. of corn, 50 Ibs. af Penka Initial wt. 149 Ibs.’ 
| f middlinas per | reer 
and lI7!bs. ao gain gS p Ny gain l.13Ibs. 


294 Ibs. of corn, 52 Ibs. of an woge \ initial wt. 146 Ibs. 
and 60Ibs. of oals per !00Ibs.gain J Av.daily gain LOT Ibs. 


eed bill for lot }4 ons of Sd 
7 , ~ oli», O m ings an 
| Besiton ot oats middlings SUS SHI 





$125 
$120 $60 
$115 
$110 $55 
$105 
$100 $50 
$95 
$90 $45 
$85 
$80 $40 
$75 
70 #35 
$65 
$60 $30 
#55 

As ze 70 60 20 1.00 “hehe ss Pysioet \. Eo” Zar ae ped oe 1.70 1.80 1.90 ei 

$25 #30 $35 $40 $45 $5 $55 $60 $65 $70 


Oats per bu. oats per ton 


30 35% 40% 45¢ 50¢ 55% Got 65 70+ 75% g@0f ire 90¢ 95% 41,00 


$20 $25 $30 $35 $40 $45 $50 $55 - $60 


FIG. 10 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 303 


CHARTS INVOLVING MORE THAN THREE VARIABLE 
FACTORS 


Rations containing three or more feeds, or, more generally, form- 
ulas involving the summation of three or more terms, may be solved 
by a method similar to that shown in the charts just considered. 


ILLUSTRATIONS IN MILK PRODUCTION 


In Fig. 11 the cost of milk per hundredweight on the herd basis 
may be computed from a formula proposed by Pearson of the Illinois 
Experiment Station, involving five items (four feeds and a certain 
amount of man labor). On the left is the scale for the labor cost per 
hour. On the right is a line graduated on the outside according to the 
price of the three types of roughage per ton, and on the inside accord- 
ing to the price of grain per ton. The body of the chart contains three 
ungraduated lines and one line graduated to indicate the total cost of 
milk per hundredweight. In determining the intersections on the 
ungraduated lines in this chart, the items are taken in the order: man 
labor hours; dry roughage other than hay; hay; grain; and silage. 
The series of dotted lines traversing the chart indicate the method of 
computing the cost of milk for the following items of cost: 


MUM ene et as elally cede eve Gk aiken ote Wise 4) cents per hour 
Pry roughage other than hay. ...........-..$19 per ton 
RES 5 SES Rea A So er ee ae 25 per ton 
OTE PCM et ayh RG Seagie oe aac aaa ie Oe ea nr $60 per ton 
STUER Sr 9 Col Bene 7h Be pe a a $10 per ton 


The total cost of milk, at these prices, is about $4.04, as is indicated 
by the intersection point of the last dotted line on the milk-cost scale. 

In Fig. 12 the cost of milk may be computed according to a second 
formula of Pearson’s, in which is considered only the expenses involv- 
ing the individual cow. The total of the items given at the head of 
the chart, however, account for only 79.58 percent of the total cost. 
The seale given for the cost of milk per hundredweight is therefore 
drawn so as to add to the sum of the five specified items 25.6 percent, 
in order that the total cost may be indicated. The use of this chart is 
then equivalent to performing five multiplications and additions and 
one division. The saving of time and mental effort is considerable in 
this case, and the result finally secured may be read off the scale with 
errors of only one or two cents at the most. With a larger chart the 
final result could undoubtedly be read off to the cent. The dotted lines 
on this chart indicate the method of computing the cost of milk, on the 
cow basis, with the prices given above. The result obtained is $4.12. 





304 ~ Beir No. 234 [ October, 

The values obtained by the use of Figs. 11 and 12 represent the 
average annual cost of milk per hundredweight. The average monthly 
cost, expressed in terms of its percentage relation to the average yearly 
cost, according to Pearson, varies from 70.6 percent in June to 120.3 
pereent in December. Fig. 13 enables one to compute readily this 
average cost for any month on the basis of any annual aver- 
age. Thus, on the basis of an average annual cost of $4.03, the aver- 
age monthly cost for February is obtained by connecting with a 
straight-edge the February mark on the left-hand scale and the $4.03 
mark on the inclined seale, as indicated by the upper dotted line. The 
monthly average is then read off the right-hand vertical scale at the 
point of intersection; i. e., $4.62. Similarly, for the month of July 
the average cost would be $3.38 when the average annual cost is $4.03, 
as indicated by the second dotted line. A chart of this character thus 
accomplishes graphically the mathematical processes of multiplication 
or of division. 


ILLUSTRATIONS IN STEER FEEDING 


By means of Fig. 14 a feed bill involving four feeds may be esti- 
mated and the necessary margin computed. The broken line 
traversing the chart from the corn-silage scale to the seale for the 
feed bill indicates the method of calculating the feed bill for the 
following prices: silage $9 per ton, alfalfa hay $28, cottonseed 
meal $75, and corn $1.50 per bushel (or $53.60 per ton; see con- 
version scale in Fig. 10). The feed bill at these prices is a little over 
$95 per head, say $95.10. Now if the straight-edge is placed at this 
point on the feed-bill scale, and at $11.50 on the cost of feeder scale 
(the outer graduation of the line at the right), the point of inter- 
section on the seale of necessary margin indicates a necessary margin 
of $3.77. 

Fig. 15 gives a similar financial interpretation of the experience of 
the last ten years at the Purdue Experiment Station with a ration of 
shelled corn, cottonseed meal, corn silage, and clover hay, for the fat- 
tening of feeder steers weighing roughly 900 to 1,100 pounds. In this 
case, with corn silage at $9, clover hay at $34, cottonseed meal at $75, 
and corn at $53.60 ($1.50 per bushel), the feed bill for five months is 
$96. With feeders at $11.50 per hundredweight, the necessary margin 
in this case is $4.02. The perpendicular seale at the side of the chart 
takes the calculations a step further, enabling one to compute the profit 
or loss per steer for any given selling price. Suppose the steers sold 
for $17.65 per hundredweight. This represents an actual margin of 
$6.15, exceeding the necessary margin by $2.13. From the side scale, 


* Pearson, F. A. The Cost of Milk Production Computed on the Year pa 
Ill. Agr. Exp. Sta. Bul. 216. 1919. See page 356. 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS ~ 305 


° 


ILLINOIS BuLtetin No. 216. Cost of Mitwk PRopucTion 


CALCULATION OF AVERAGE. COST OF MILK PERCwT. 
PER YEAR ON THE HERD Basis meee 


ITEMS IN GENERAL FoRMULA UseD roughage per ton 

Grain 44 lbs Hay 50lbs 

Silage |88lbs. Other roughage 39lbs. 
Man labor 242 hrs 





Price of grain 
Hay Grain per $on 
Dry 30 30 
Roughage Silage 
other than hay 3 
Man labor 
er hour Cost of milk 
p per cwl. 25 
$7.00 
60 
50 
70 600 
20 
50 
60 
5,00 
“XN — cA 
ote ae < 50 
~ 
50 On - Make 15 
~ 
nse 4.00 
wa 
ae 50 
Se =e ye 
7, 
3,00 
10 
po. @) 50 
2.00 
20 
50 5 
1.00 


PYG. 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 


ILLinois Buttetin No. 216. Cost or Mick Proouction 
CALCULATION OF AVERAGE CosT oF MILK PER 
CwT PER YEAR ON THE Cow BASIS 


307 


Price of roughage 


per ton 
ITEMS IN GENERAL FORMULA USED: 
Grain 55 Ibs. Hay 36 lbs. 
Silage I40lbs, Other roughage 22 lbs. 
Man labor 2.36hrs. 
Price of $30 
grain per 
ton 
Pea age other 
jan hay and silage Silage Hay ane Ae 
Man _ labor tar 
osTo 
Reon milk per ewt $75 $25 
80% $7.00 
$70 
59 
$65 
70% 
$6.00 
$60 $20 
60! a $55 
eu #50 
50? ES $45 $15 
Ts 
Lice #400 $40 
Wee 
40 — 
eee aS 7 50 $35 
50 
= $25 
$2.00 $20 
20* 
$15 $5 


FIG.J2 


moat 
, 
‘ 
. 
5 Sen tee te 
. 
' 
5 
- 


‘ 


- 
OP ee / 
oe 7 o 

ey | 
he # 

od. . 7 rT 

P.) 4 - 


, 
i 
rege rioe 2 
y- 
-—_, 
¢ 
- 
i 
y 
Saha toa 
Z 
; 
: 


— ——F 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 309 


ILLINOIS Buttetin No.2I6. Cost or Mick Propuction 


CALCULATION OF AVERAGE MONTHLY Cost oF MILK PER 
Cwr. FRom AVERAGE YEARLY Cost 


Average monthly 
cost per cwt 





FIG.I3 


f 
i 





ee 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 311 


Missouri BuLceTin No.I50. STEER FEEDING 
CALCULATION OF FEED BILL AND NECESSARY MARGIN 
OF STEER FATTENING OPERATION 
Lor | (SEconp TriaL) INITIAL Weight 925 LBs. 

GAIN of 394 Bs. In 130 Days 



















Tota. Feep Consumed PER STEER: PRICE OF 
HAY PER 
SHELLED CORN. 2173 -eBs Price Ton AND 
Cottonseeo Meau oles yr CosT OF 
25 : OF CORN 
Corn SILace 3867 AND [| FEEDERS 
ALFALFA Hay A235 COTTON L PER OWT: 
$5.00 SEED [-”” 
MEAL Set 
_ PER 
31 
ALFALFA COTTONSEED Corn aoe 
so [HAY MEAL $ 90 $50 
25 $170 85° 
i 160 eo 
ex, |50 
75 
~~ 
~~ 140 
50 ma 
aN os 
N c 
ae Wl {30 
PRICE 25 “= a tu 
OF 8 H 
CORN 7K 300 ag 120 
SILAGE 5 ie 4 
PER > aes ae 10 
TON: > t—=75 acs 
ea i ee 100 
<[—s50 a 
ie@4 Ww Slee 
: shee 
$15 OF ,. Pane ou case 
wl Papest i 
(ae peas 
2.00 Pig 80 
{3 a 4 
Po 
12 ah 
A a . 70 
n Kb 
a 
10 . 60 
eg 
9 
aa 
é 7 50 
ts 1.00 40 
6 
5 30 


FIG. 14 





* 
' . 
< 
‘ 
a 
. 
: 
2 
= 
ee ~ 
® 
tee 
7 
— 
. 
~~ 
ere 4 and: 
~ 
t 
w 
~— 
es + 
Mntr 
. 
' 
“~~ 





and 
“ 
Par 
os 
‘ 

' 


7 
~ 
~ 








1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 313 


Puroue. ExrerRiMeENnt STATION 


CHART BASED ON AVERAGE OF TEN YEARS EXPERIENCE IN 
FATTENING STEERS ON A RATION OF SHELLED CORN, COTTONSEED 
MEAL, CoRN SILAGE, AND CLOVER HAY 


IOOO LB. FEEDERS, GAINING SGOLBS. DURING A FATTENING PERIOD OF [50 DAYS 
AVERAGE FEED CONSUMED PER STEER 


Daily Total 
Shelled corn 12.98 lbs. 0273 ton Price of clover hay 
Cottonseed meal ato] Diente 0210 - per ton and cost of 
Corn silage 28.85 ” 2.162 Derararen cw 
20-4 Clover hay S4)] ° UY dole Weg f 
a 
7 : 
235 : 
H Price of corn and : 
Aa cottonseed meal 8355 
6 per _ton 
ry 
%— Clover yet 4 
hay hellea corn . 
Cotton seed meal aA. 190 954 
i 2 
. 160 20 $30 
$5 8 
170 85 3 
7: 
160 60 
150 75 25 
£ 
140 5g 
$4—4 70 g 
€ ae 8 
ieee c “ 2 *. 38 in 
of corn ” : Dai 0 
=, 120 
silage = ~ A 60 200 © 
er-ton| > ma Q = = 
| 2 ae Te 55, o 
= ae 
ba = Go o 
3 ee Se geen 8 
50 = a4 
od ep pat ee 8 On 
ey, yen EH coe 5 N6 
$154 Oo pst eat he &E 9 45 Ise = 
el lhe Se © fe) 
o a = g o 
Seid i) 80 40 = 
3 0 2 JP ° 8 
Bed |Z . 3 
%, 70 35 o* 
14 Z 5 
$10 ry, : 60 30 eee “2 
al a 
- 50 25 
e 40 20 
6 ry 
$5 30 15 5 
4 ° ° 
3 $0 


FIG.IS 


— 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 315 


we then find that when the difference between the actual and the 
necessary margins is $2.13, the profit per steer is $29. Obviously, if 
the steers sold at the necessary margin, no profit would be realized, 
while if the selling price had been at a margin of, say $3.75, twenty- 
seven cents less than the necessary margin, the loss would be, according 
to the same scale, about $3.70 per head. 


CHARTS PERMITTING GREATER FLEXIBILITY IN 
FINANCIAL PREDICTIONS 


The chart just described, constituting a financial interpretation of 
experimental results at the Purdue Station, is flexible as far as vari- 
ations in market conditions for live stock and feeds is concerned, but 
it is nevertheless too rigid to meet all conditions confronting the 
live-stock man desiring to profit by this valuable experimental work. 
The rigidity impairing the universal usefulness of the chart is due to 
the fact that no variation is possible in the weight of feeder steers or in 
the gain secured. It would of course, be impossible for a farmer to 
secure feeders weighing just 1,000 pounds. In fact, variations of 100 
or 200 pounds from this figure would many times be unavoidable. And 
yet any variation would influence the necessary margin or the esti- 
mated profits. This fact, perhaps, is not emphasized fully enough in 
experiment station bulletins. Feeder steers bought on the market will 
vary from 850 to 1,150 or 1,200 pounds, and it cannot be assumed that 
animals of any given average weight can be secured as desired. Again, 
if feeder animals as secured on the market, varying from 850 to 1,150 
pounds, are fed the daily ration prescribed in the manner prescribed, it 
cannot be expected that at all times gains will be secured at the aver- 
age rate of 2.4 pounds per head. As a matter of fact, the results at 
Purdue during the last ten years, obtained from lots of ten animals, 
have shown gains varying from 2.02 to 2.63 pounds per day, or 303 to 
394 pounds in five months of feeding. Of course, a variation in the 
gains secured may materially affect the necessary margin. 


ILLUSTRATIONS IN STEER. KEEDING 


A chart that permits of flexibility in financial interpretation along 
the lines mentioned is presented as Fig. 16. The use of the chart is 
illustrated by the broken transverse lines, involving the same prices 
and experimental data as Fig. 15; 1. e., feeders at $11.50 per 100 
pounds, a gain of 360 pounds, a feed bill of $96 per head, and a final 
weight of 1,360 pounds. A straight-edge placed at the $11.50 mark 
on the cost-of-feeder scale at the extreme left, and at the 360-pound 
mark on the inclined seale for gains in weight, is extended to intersect 
the vertical to the immediate right, and the point of intersection is 


316 BULLETIN No. 234 [ October, 


indicated in light pencil. This point is then connected by a straight- 
edge with the $96 mark on the feed-bill scale at the extreme right. 
The point of intersection on the ungraduated vertical line just to the 
left of the latter scale is then marked in pencil. The straight-edge is 
then revolved until it passes thru this point and the 1,360-pound mark 
on the scale of final weights of steers. This line cuts the intermediate 
inclined line at the $4.02 mark, thus indicating the necessary margin 
and duplicating the determination made with Fig. 15. If, however, 
the feeder steers had been bought at 900 instead of 1,000 pounds, it 
may be shown from the chart that the necessary margin would have 
been $4.36; if bought at 800 pounds, it would have been $4.73; or at 
1,100 pounds, $3.16; in all cases assuming a gain of 360 pounds. 
With 1,000 pound feeders and a gain of only 300 pounds, the necessary 
margin is $4.54; or with a gain of 400 pounds, $3.68. A farmer can- 
not, of course, make a better prediction of the gains he will secure with 
a given ration than the experiment station whose directions he is fol- 
lowing, but if after two or three months of feeding the ration, his 
daily gains are much greater or less than those which the experiment 
station secured, he may modify his prediction, and, with the aid of 
this chart, his estimated necessary margin. 

Fig. 17 permits a further step in financial computations. If with 
the aid of a feed-bill chart and Fig. 16, a certain necessary margin is 
computed, the fattening operation is about completed, and the stock 
man wishes to compute probable profits in view of prevailing prices 
on the live-stock market, this chart will be of aid. Suppose that with 
885-pound feeders costing $10.43 his estimated necessary margin is 
$4.92 and that the probable gain at the end of the five months of feed- 
ing will be 375 pounds. Suppose further that beef such as he expects 
to produce is selling on the market for $17.50; i. e., at a margin of 
$7.07. This figure is $2.15 above his necessary margin. Now by using 
Fig. 17, and connecting the point 1,260 (885+875) on the left seale 
of final weight of steers, with $2.15 on the inclined seale, his profit, 
if he secures the above price for his beef, would be indicated by the 
intersection point on the right vertical scale; namely, as $27.12. 


SUGGESTIONS FOR INCREASING THE PRECISION OF 
FINANCIAL -ESTIMATES 


In the discussion thus far it has been assumed, as is generally 
done, that the receipts in feeding operations include only the net 
returns (as defined on page 274) from the sale of the animals, and 
that the expenditures include the feed bill only. Some of the incidental 
expenses are of course allowed for if the cost of feeders is taken to 
mean the cost in the feed lot and the margin to mean the margin of 


mw THe Pao 
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ik. Pitcay: Viiwee, oF het % 

















hive eer 








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tain | 
Re Pasion, “fey 


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€ a st 
‘ 


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“4 ma Os 
oie | be jew 


f | E. ere 


ee 
te 
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ee eee Eh oe as pea SA 





i 
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6 
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ee 
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aa aya ; ry ie? , } 


enasts 





CALCULATION OF NECESSARY MARGIN OF STEER FEEDING OPERATION FOR 
VARYING Cost oF FeeperS, GAIN SecurEp, FEED BILL. AND FINAL WEIGHT 
OF STEERS 


CALCULATION OF THE PRoFIT oR Loss PER HEAD 
IN STEER FEEDING OPERATIONS FROM: 
1. THe FinAL WEIGHT oF THE STEER,AND 
2. THE DIFFERENCE BETWEEN THE ACTUAL AND 


50 Necessary Marcins 






Bet Ea 
$8 
1350 
504 |= = 
E o : | 
: iG x 1300 a 
940 Wd s =; 
Seeks : e 
= ee See : 
304 Wd su : 
a ‘ 


—— 


off at 





30 


Vi El Gott ae 






Uo i ts BAN) Eo 
Omid eu Ee Est) 


50 





FIG.AT 





FIG.I6 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 317 


selling price minus shipping and other incidental expenses, over the 
eost of the feeders in the feed lot. However, other receipts than the 
net cash receipts from the sale of animals, such as manure and pork 
produced from the same, must be recognized, as must also other ex- 
penditures than the feed bill, mainly labor, interest, insurance, and 
taxes. The frequent assumption that the value of manure produced 
offsets the cost of labor is obviously unsatisfactory. Of greater weight 
is the conclusion reached in the recent statistical résumé of the meat 
situation in this country’ to the effect that in baby beef production the 
manure and the pork produced almost exactly offset items of expendi- 
ture other than feed; but even this conclusion must be discounted in 
view of the lack of system in the method employed of evaluating the 
manure, a procedure which was left entirely to the unaided judgment 
of the live-stock farmer. It would seem advisable in feeding experi- 
ments to determine as precisely as practicable the amount of manure 
produced, its average composition, and its fertilizing value. The collec- 
tion of the manure should conform only to the best farm practice in 
collecting manure for distribution as fertilizer on the fields. Only in 
this way can an accurate estimation of the value of this important item 
in feeding operations be obtained. 

The frequent practice among experiment stations of crediting all 
pork profits from undigested corn to the steer feeding operation, re- 
gardless of the additional corn or supplemental feeds given the hogs, 
the cost of the latter feeds being deducted from the value of the pork 
produced, is unsound from every standpoint. Only when check lots of 
hogs, fed the same way except for the access to steer droppings, are 
employed, can the actual amount of corn thus utilized, the actual 
amount of pork produced, and the actual profits realized from this 
practice be determined (see Iowa Exp. Sta. Bul. 182). When this is 
done, the results may, perhaps, best be stated as a given amount of 
pork per bushel of corn in the ration. (Purdue Exp. Sta. Bul. 146, 
page 605). 

Another difficulty in the proper financial interpretation of feeding 
operations is the evaluation of home-grown feeds of no definite market 
value. Among these feeds silage is of great importance, figuring largely 
in steer feeding operations especially. And yet, as far as the author is 
aware, there is no systematic or commonly recognized method of valu- 
ing this feed. Investigation along this line is undoubtedly needed, that 
it may be ascertained whether there is any close relation between the 
yield of corn per acre (and possibly its composition) and the amount 
of corn per ton of silage—to the end that some fair relation may be 
determined, if possible, between the price of corn and the inherent 
value of silage. Much of the current discussion as to whether it is 
profitable to feed corn in rations containing corn silage fed ad libitum, 


*U. S. Dept. Agr., Report No. 111, Part ITI, pages 62-63. 1916. 


318 } BULLETIN No. 234 [ October, 


properly supplemented with hay and a nitrogenous concentrate, is of 
doubtful significance unless a satisfactory method of valuing the silage 
can be agreed upon, since when the corn is not fed the consumption 
of silage is enormously increased and becomes an important item in the 
feed bill. 


APPENDIX 


Construction of Fig. 1 


This type of alignment chart is suitable for the solution of all 
equations of the form 


aP + bQ = R, or aP — bQ = R, 


where P, Q, and R are any functions of three variables. The scales 
for P and Q are the outside scales, while the scale for R is situated 
somewhere between them. The general equation for its location is 

bpk 
aq -- bp >. 
where x is the distance between the scales for P, on the left, and for 
R; k is the distance between the scales for P and Q; a and b are the 
constants in the above equation; and p and q are the unit distances 
(moduli) on the seales for P and Q, respectively. 

The side scales are placed at some arbitrary convenient distance 
apart, and a reasonable range of values laid off on each, choosing a 
convenient unit distance, or modulus, for the dollar in each case. In 
choosing these units, consideration should be given the fact that, ac- 
cording to the equation from which the values on the intermediate 
scale are to be computed, 1. e., 


ge+ (w+g)m=—r, rae 
the margin, m, dollar for dollar, is a more important determinant of 
r than is the cost of calves, ec. Hence its unit should be larger. 
Having constructed the two side scales, the distance between the 
left scale and the intermediate scale is computed from the relation 


ee We (2) 
gm’ + (w-+ @) @” 
in which x is the distance desired; ¢’ is the distance chosen to represent 
a dollar on the left-hand seale; k is the distance between the two side 
scales; m’ is the distance chosen to represent a dollar on the right-hand 
scale (the modulus) ; and w and g have the same significance as in the 
preceding equation. (See Deming’s Manual, page 38; also Lipka, 
Graphical...Computations, pages 44-64.) Having located the posi- 
tion of the intermediate scale, two points fairly wide apart, say those 


x 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 319 


for $85 and $150, are located on it by long-hand calculation of equation 
(1), using a straight-edge to connect the values taken for selling price 
of calves and margin. The distance between these two points is then 
divided into the proper number of equal parts, in this case 65. (See 
Deming, page 23.) 


Construction of Fig. 2 


This chart is similar in general to Fig. 1. In the case of Lot 1, for 
instance, the equation for the feed bill is 

x == 1.993 times the price of corn -++ 0.0552 times the price of 
alfalfa hay. 

The location of the intermediate scale for this lot is given by 


ut 0.0552 ct k 
~ 1,998 at + 0.0552 ct’ 


in which x is the distance from the left-hand scale to the scale for 
Lot 1; ¢1, the distance representing one dollar on the left-hand scale; 
k, the distance between the two side scales; and a, the distance repre- 
senting one dollar on the right-hand scale. 

The seales for the other lots are similarly located. Good judgment 
should be shown in choosing suitable values for c! and a!. A glance 
at the rations given at the head of the chart shows that a dollar’s vari- 
ation in the price of corn exerts 10 to 75 times as great an effect on 
the feed bill as a dollar’s variation in the price of alfalfa hay. The 
units chosen should therefore stand in a somewhat similar relation in 
order to insure a proper centering of the intermediate scales and a 
consequent greater accuracy in their use. 

With the intermediate scales thus located, definite points on each 
are found by direct calculation and the use of a ruler or string, and 
the distances between points on any one scale are divided into the 
proper number of equal parts in determining the dollar unit distance 
for each scale. 


Construction of Figs. 3 and 4 
No additional instructions need be given for these charts. The 
directions and formulas given for Fig. 1 apply here. 
Construction of Fig. 5 
The construction of this chart is similar to that of Fig. 1. Equation 
(2) is used in locating the intermediate scales, varying k as required. 
Construction of Fig. 6 


After setting up the two extreme side seales for the price of corn 
and the price of supplements, the intermediate scales are located and 
graduated in the usual way. Points on the ‘‘corn-alone’’ scale are 


320 BULLETIN No. 234 [October, 


located as follows: 486.5 pounds of corn are equivalent to 8.69 bushel. 
The $18 mark is located on the corn price scale by simple division of 
this figure by 8.69; similarly to $5 mark. The difference between these 
two points is then divided into 65 equal parts for a 20-cent interval. 
The location of an intermediate scale is accomplished as follows. The 
eorn-and-oil-meal ration calls for 377.3 pounds of corn and 51.7 pounds 
of oil meal, or 6.74 bushel of corn and 0.02585 ton of oil meal. The 
equation to be solved is therefore 


6.74 ¢ + 0.02585 o = r, 


where ¢ is the price of corn per bushel and o is the price of oil meal 
per ton. The distance between the corn price scale on the left and the 
intermediate scale desired is 


0.02585 ¢1 k 
6.74 01 + 0.02585 c!’ 


pq eS 


where c! is the distance taken to represent one dollar on the corn price 
scale; o!, the equivalent distance on the supplement scale; and k, the 
distance between the two extreme scales. Points on the intermediate 
line thus located are best found by connecting points on the two outer 
scales corresponding to even dollar values for r, according to the 
above equation. 


Construction of Figs. 7 and 8 


No additional instructions need be given for these charts. The 
directions given for Fig. 6 apply here. 


Construction of Fig. 9 


Just as the graphical solution of an equation of the first degree for 
one variable in terms of two others may be carried out with a triple- 
parallel chart, so the graphical solution of a linear equation for one 
variable in terms of any number of other variables, such as . 


aw + bx+cy+dz+...=r, 


may be carried out by a chart such as this. In this series of functions, 
a, b, e, d, ete., are constants, representing, in the present case, the 
weights of feeds consumed; while w, x, y, z, ete., are variables or func- 
tions of variables representing in the present case the prices of feeds. 
A chart for the summation of such terms is constructed by setting up 
at the extreme right a scale for the variables, and at intervals per- 
pendicular lines, the distance of each of which from the left scale is 
proportional to the reciprocal of the sum of the constants in the above 
equations up to and including the term in question. Thus, in the 


1921]. FINANCIAL PHASES OF FEEDING EXPERIMENTS 321 


equation given there would be four uprights, at distances from the ioe 
hand scale proportional to 


1 1 1 aay fi 
a oatb a-bte Abed: 
In the present case the equation of the feed bill of Lot 2, involv- 
ing 3 feeds, is 


r = 0.250 x + 0.168 y + 3.255 z, 


in which x is the price per ton of clover hay, y the price per ton of 
cottonseed meal, and z the price per ton of corn silage. In the con- 
struction of feed-bill charts it is often inconvenient, on account of the 
ereat disparity in the price of feeds, to use the same seale for all 
feeds, according to the unmodified plan. For example, roughages are 
ordinarily much cheaper per ton than cereals and nitrogenous concen- 
trates, and their price scale should therefore have a greater unit dis- 
tance for the dollar. Technically speaking, the modulus of the rough- 
age scale should be greater than that of the concentrate scale. And 
this may be accomplished by multiplying or dividing the constant 
coefficient according as the modulus of the corresponding price seale is 
decreased or enlarged. In the present instance, taking the standard 
price scale as that suitable for cottonseed meal, it is advisable to in- 
crease the modulus of the price scale for clover hay by twice, so that 
the corresponding coefficient is divided by two. Furthermore, it was 
decided to value the corn silage per ton at 6.5 times the price of corn 
per bushel; that is 1 ton of corn silage equals in price 364 pounds, or 
0.182 ton, of corn. The corn price scale is made the sameé as'the cotton- 
seed meal price scale. The above equation is changed, therefore, to 


r= 0,125'x + 0.168 y + [(3.255) (.182) = 0.592] 21, 


where z! is the price of corn per ton. The chart for Lot 2 consists of 
the scale at the right for corn and cottonseed meal, and three per- 
pendicular lines situated at distances from the scale proportional to 
the reciprocals of 0.125, (0.125 + 0.168 =) 0.298, and (0.293 -+- 
0.592 —) 0.885. It will be noticed that the clover-hay price scale given 
on the first line at the left of the chart for Lot 2 has a modulus twice 
that of the right-hand scale and is arranged so that a given distance 
above the base line represents a price just half that at an equal height 
on the right-hand seale. The cottonseed-meal upright is not graduated 
but the corn line is graduated to represent the stat feed bill. This 
scale is readily constructed since its modulus is 74¢5 times that of 
the principal scale on the right. The $30 mark on the feed-bill scale, 
for example, is at the same level as the (30 ~ 0.885 —) $33.90 mark 
on principal scale. Two extreme points can be thus located on this 
seale, and then the distance between these points divided into the 
proper number of equal parts, 


522 BULLETIN No. 234 [ October, 


The chart for Lot 1, to the left of the chart just considered, is con- 
structed in a similar way. If the price of corn silage can be based on 
the price of corn, as is here done, the four feeds of Lot 1 may be 
charted as three feeds. The equation to be solved is 


r = 0.240 x + 0.168 y + 2.841 z 4+ 0.249 z}, 


where x, y, z, and z! have the same significance as above. Pricing corn 
silage per ton at 6.5 times the price of corn per bushel, the last two 
terms can be combined. The clover-hay modulus is increased by twice 
and the coefficient correspondingly divided by two, so that the modified 
equation is 


r = 0.120 x + 0.168 y + [(2.841) (0.182) = 0.517 + .249 =] 0.766 2’. 


In this case the $30 mark on the feed-bill scale is at the same level as 
the (30 — 1.054 —) $28.46 mark on the principal scale, since the sum 
of the coefficients in the above equation is 1.054. 

Charts such as those just described, involving a reciprocal hori- 
zontal seale, are described in Deming’s Manual, pages 47 to 50, for the 
first time. Their use in the present instance is described in the 
Text 

The horizontal seale at the bottom of the chart, for the conversion 
of prices of corn per bushel into prices per ton, is very simple in con- 
struction. Since a bushel of corn is equal to 334,; ton, each point on 
the lower graduation equals 35.71 times the corresponding point on the 
upper graduation. The seale is conveniently made by first laying off 
the upper scale, using any convenient modulus, and then locating two 
extreme points on the lower seale. Thus, the $40 mark on the lower 
scale coincides with the (40 -—- 35.71 —) $1.12 mark on the upper. 
The distance between the two points thus loeated is divided into a 
convenient number of parts. 


Construction of Fig. 10 


No new principles are involved, aside from the superposition of 
two charts. For Lot 14, the feed-bill equation is 


0,025 x + 0.0585 y + 0.145 z =r, 


where x is the price of tankage; y, the price of middlings; and z, the 
price of corn per ton. The tankage price seale, given on the left, is 
taken as the standard, and the other scales for middlings and corn are 
constructed with a modulus twice as large as that of the tankage scale, 
and in such a way that any given price on the one seale is at the same 
level above the base line as twice that price on the other scale. Hence 
the coefficients for corn and middlings must be divided by two, and 
the equation reduces to 


r = 0.025 x + 0.0292 y + 0.0725 z. 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 323 


The distances from the tankage scale to the principal scale on the 
right, from the middlings ungraduated perpendicular to the same 
scale, and from the perpendicular bearing the feed bill for Lot 14 per 
100 pounds of pork, to the right-hand scale, stand to each other in the 
proportion of the reciprocals of 0.025, (0.025 + 0.0292 —) 0.0542, and 
(0.0542 + 0.0725 —) 0.1267. The feed-bill scale for Lot 14 is such 
that any price on it, say a, is at the same level above the base line as 
a —- 0.1267 on the tankage price seale. 

Lot 15 is charted in an exactly similar manner, the same side scales 
being used for the price of feeds, and the two intermediate lines being 
located, one ungraduated for oats, and the other so graduated for corn 
as to give the total feed bill. 

The corn conversion seale at the bottom is constructed as already 
explained. The oat conversion scale is constructed similarly, tho in 
this case each point on the lower graduation is (2000 + 32—) 62.5 
times the coincident point on the upper graduation. 


Construction of Fig. 11 
The equation to be solved in this ease is 
2.42 v + 0.0195 w + 0.025 x + 0.022 y + 0.094 z—r, 


in which the variables are the cost of man labor per hour and the 
prices per ton of roughage other than hay or silage, hay, grain, and 
silage, respectively. The standard scale adopted is that for roughage, 
all three types, this scale being set up on the outside of the line on the 
extreme right. The modulus for the labor scale is 30 times that of the 
standard, and the scale will be found at the extreme left of the chart. 
Each value on this scale is at the same level as 30 times its value on 
the standard scale. The modulus for the grain scale is taken as one- 
third of the standard modulus. This scale is laid off on the inner side 
of the line at the extreme right of the chart. The above equation then 
reduces to 


0.0807 v + 0.0195 w + 0.025 x + 0.066 y + 0.094 2=r. 


The five lines to the left of the standard seale are at distances from 
it proportional to the reciprocals of : 


Bera Or SGT. DOUT sales, side tt, 4 ate ove < 0.0807 
Roughage other than hay and silage.... (0.0807 + 0.0195 —) 0.1002 
Le A, Ne porte RN a nerd a Rah a se (0.1002 + 0.0250 —) 0.1252 
Syren Sha eee oe tees cuter, nica eae 3s, « (0.1252 + 0.0660 —) 0.1912 
SNE CAE Wee ade ena Mage ea ae ar (0.1912 + 0.0940 —) 0.2852 


and each value on the scale representing the cost of milk per hundred- 
weight is therefore equal to 0.2852 times the value at the same level on 
the standard scale. 


324 BULLETIN No. 234 [ October, 


Construction of Fig. 12 


In this case the sum of the coefficients, after price adjustments are 
made in the same manner as in Fig. 11, is 0.2337. However, since the 
sum of the five items enumerated in this case is only 79.58 percent of 
the total cost of the milk, this figure is divided by 0.7958, giving 0.2937. 
Hence any value on the seale representing the cost of milk per hun- 
dredweight is at the same level as 0.2937 times that on the standard 
scale. To be more specific, the $4.00 point on the former seale is at 
the same level as the ($4.00 + 0.2937 =) $13.62 point on the standard 
scale at the right. 


Construction of Fig. 13 


This is a transversal alignment chart suitable for multiplying or 
dividing. In this case, multiplication is accomplished. The equation 
to be solved is 

pT ih 


where x is the ratio of the average price of milk for a given month 
to the average price per year; y is the average annual price of milk; 
and r is the average monthly price of milk. A uniform percentage 
seale (x) is laid off at the left from 70.6, the lowest percentage (for 
June), to 120.8, the highest percentage (for December). Instead of 
indicating percentages on this scale it is sufficient to indicate the 
name of the month at its proper position on the seale. At the right 
a uniform scale is laid off for the monthly cost of milk per hundred- 
weight (r), a range from $1 to $8 being ample. The cross-line con- 
nects the zero points on both of the side seales. In ease the zero point 
on one or both scales is so far removed as to make mechanical connec- 
tion inconvenient or impossible, the inclined intermediate scale may 
be located by geometry (see Deming, page 33). The scale on the in- 
clined line is not uniform, but projective. It may be laid off by locat- 
ing, by the use of a straight-edge, two extreme points and one inter- 
mediate point midway between the other two. The points of inter- 
section of any straight line on the inclined line (y) and on the two 
parallel lines (x and r) stand to each other in the relation indicated 
by the above equation. From the three points thus located the scale 
may be laid off by geometric means (see Deming, page 23). For a 
further discussion of transversal alignment charts see Deming’s 
‘‘Manual,’’ pages 39 to 43, and Lipka’s ‘‘Graphical and Mechanical 
Computation,’’ pages 65 to 87. 


Construction of Fig. 14 


This chart is concerned, first with the calculation of the feed bill for 
the ration indicated at the top; and second, on the basis of this result 


1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 325 


and the cost of feeders, the calculation of the necessary margin when 
the initial weight of feeders and the gain are as indicated. 

The scales to be used in the determination of the feed bill involve 
no new principle. The standard price scale is taken as that for alfalfa 
hay and corn silage. The modulus for the corn and cottonseed-meal 
scales is one-third that of the standard, so that each value on this scale, 
laid off on the inside of the line at the extreme right of the chart, 
coincides with a value one-third as great on the standard seale, laid 
off on the outer side of the same line. The original feed-bill equation, 


r= 1.933 w + 0.2115 x + 0.181 y + 1.0865 z, 


in which w is the price of corn silage per ton; x, that of alfalfa hay ; 
y, that of cottonseed meal; and z, that of corn; becomes, on making the 
above scale adjustments, 


r = 1.933 w + 0.2115 x + 0.543 y + 3.2595 z. 


If from the feed bill thus determined is subtracted the product of 
the gain secured, expressed in hundredweight, and the cost of feeders, 
and the difference is divided by the final weight of the steers in hun- 
dredweight, the quotient is the necessary margin. Now the process of 
subtraction is performed on a chart of this character by working back- 
wards from right to left, just as summation is accomplished by work- 
ing from left to right. In this chart the vertical lines for the different 
feeds are located as usual, their distances from the standard scale 
being proportional to the reciprocals of the following numbers: 


PPPS Cr teow Som ence leat se gh oan, oh ose ial, Wah Ske eew ISS 1.933 
Pe VTE LY | Wate te iette oi als nix sig ees iesewie's asks. ies S aS byes 2.144 
DOE SR EGO SS Soe Doe eee ar Pere GAA ae 2.687 
ESS 9 Ao ee aig ris roe inane age ee a ae 5.946 


and the feed-bill scale on the corn upright, at any level, contains values 
5.946 times the corresponding value on the standard scale. The sub- 
traction of the product of gain in hundredweight and the cost of 
feeders, 3.94 v, the standard scale being used for the cost of the 
feeders, locates a vertical scale removed from the standard scale by a 
distance proportional to the reciprocal of 5.946 — 3.94 — 2.006. 
Dividing this number by 13.19, the final weight in hundredweight, we 
get 0.1521. Hence any value on the scale of necessary margin equals 
0.1521 times the value on the standard scale at the same level. Thus 
the $10 mark on the standard scale is at the same level as the $1.52 
mark on the necessary-margin scale. 


Construction of Pig. 15 


The construction of this chart is similar to that of Fig. 14. The 
lower horizontal scale, from which the profit or loss per steer is read 


326 BULLETIN No. 234 [October, 


off for any given difference between actual and necessary margin, de- 
pends for its construction on the following fundamental equation: 


ge -+ (w+ g) mr, 

in which g is the gain in hundredweight and w the initial weight in 
hundredweight, these being constant; while of the variables, ¢ is the 
cost of feeders, m the margin per hundredweight, and r the receipts 
per head. When r just equals the feed bill, or, more generally, the 
cost of the feeding operation, m is the necessary margin. For every 
dollar by which the actual margin at which the steers are sold exceeds 
this necessary margin, the profit secured is obviously equal to 
(w + g), or the final weight of the steer expressed in hundredweight. 
For every dollar by which the actual margin falls short of the neces- 
sary margin, a corresponding loss of (w + g) dollars must be borne. 

Hence a scale is laid off on the upper side of the horizontal line 
representing differences in dollars and cents between the actual margin 
and the necessary margin as determined by the chart. A scale may 
now be laid off on the lower side of the same line to represent the gain 
or loss realized by making each value on the latter equal to 13.6 times 
the coincident value on the former scale. If the difference between the 
actual and the necessary margins is positive, the value read off the 
lower scale represents profit; if negative, it represents a loss. 


Construction of Fig. 16 


The purpose of this chart is to facilitate the calculation of the 
necessary margin for steer feeding operations, for varying cost of 
feeders, initial weight of feeders, gain secured, and total feed bill. In 
the fundamental equation given above, if r, the net receipts per head, 
equals the feed bill, then m becomes the necessary margin and may be 
obtained by the following equation: 

f — ge 

Wwe” 
in which f is the feed bill. The left half of the chart represents a 
multiplication of gain in hundredweight and cost of feeders (see Fig. 
13). Since this result in itself has no particular significance it need 
not. be indicated by a seale, which would naturally be placed on the 
same line as the scale for the final weight of steers. The right half of 
the chart involves two mathematical operations, a subtraction and a 
division. The product secured by the multiplication of gain by cost 
of feeders is subtracted from the feed bill scaled on the line at the 
extreme right. The difference thus secured is indicated by the inter- 
section on the vertical line situated between the feed-bill scale and 
the seale of the final weight of steers. Since this difference per se 
possesses no significance, this vertical line is not graduated. It might 





1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 327 


be said here that in triple-parallel.charts, such as this, when the two 
functions involved are scaled on the outside parallels in opposite diree- 
tions, one scale increasing in value from the bottom upwards and the 
other from the top downwards, subtraction of the two functions is 
indicated by the point of intersection on the intermediate line (see 
Lipka, ‘‘Graphical Computation,’’ page 45), instead of addition, as 
when the outer scales are graduated in the same direction. The differ- 
ence obtained by the point of intersection on the intermediate vertical 
line is then divided by the final weight of the steer in hundredweight, 
the scale for which is on the same line as that used to indicate the 
product of gain and cost of feeders. A straight line from the point 
representing the difference between feed bill and the product of gain 
and cost of feeders, to the final weight of steer intersects the inter- 
mediate inclined line (for the construction of which see Fig. 13) at the 
necessary margin required. 


Construction of Fig. 17 


The construction of this chart involves the same ius inciples as are 
involved in Fig. 13 (q.v.). 


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